Texas Local Government Code - LOC GOV'T § 86.021. General Powers and Duties

(a) A constable shall execute and return as provided by law each process, warrant, and precept that is directed to the constable and is delivered by a lawful officer.  Notices required by Section 24.005, Property Code, relating to eviction actions are process for purposes of this section that may be executed by a constable.

(b) A constable may execute any civil or criminal process throughout the county in which the constable's precinct is located and in other locations as provided by the Code of Criminal Procedure or by any other law.

(c) A constable expressly authorized by statute to perform an act or service, including the service of civil or criminal process, citation, notice, warrant, subpoena, or writ, may perform the act or service anywhere in the county in which the constable's precinct is located.

(d) Regardless of the Texas Rules of Civil Procedure, all civil process may be served by a constable in the constable's county or in a county contiguous to the constable's county, except that a constable who is a party to or interested in the outcome of a suit may not serve any process related to the suit.  All civil process served by a constable at any time or place is presumed to be served in the constable's official capacity if under the law the constable may serve that process in the constable's official capacity.  A constable may not under any circumstances retain a fee paid for serving civil process in the constable's official capacity other than the constable's regular salary or compensation.  Any fee paid to a constable for serving civil process in the constable's official capacity shall be deposited with the county treasurer of the constable's county.

(e) The constable shall attend each justice court held in the precinct.